Ian Postlethwaite

Brief Linear conditioning for systems containing saturating actuators

A system composed of a linear controller and plant can exhibit strange behaviour when the actuators linking the controller to the plant are subject to saturation, or other nonlinear effects. Linear conditioning means augmenting the system with a linear transfer function to change the systems behaviour during, and immediately following, saturation. In this paper, the behaviour of linear conditioning schemes is interpreted in terms of a single transfer function M(s). This transfer function not only facilitates the understanding and comparison of conditioning schemes, but also leads to a new framework for conditioning design.

A new perspective on static and low order anti-windup synthesis

By viewing the anti-windup problem as a decoupled set of subsystems and relating this configuration to a general static anti-windup set-up, LMI conditions are established which guarantee stability and performance of the resulting closed-loop system. The approach taken, and the mapping used for the performance index, are logical and intuitive–-and, it is argued, central to the ‘true’ anti-windup objective. The approach enables one to construct static anti-windup compensators in a systematic and numerically tractable manner. The idea is extended to allow low-order anti-windup compensators to be synthesized, which, while being sub-optimal, can improve transient performance and possess several desired properties (such as low computational overhead and sensible closed-loop pole locations). In addition, low-order anti-windup synthesis is often feasible when the corresponding static synthesis is not.

Incorporating Robustness Requirements Into Antiwindup Design

This paper treats the problem of synthesizing antiwindup compensators that are able to handle plant uncertainty in addition to controller saturation. The uncertainty considered is of the frequency-weighted additive type, often encountered in linear robust control theory, and representative of a wide variety of uncertainty encountered in practice. The main results show how existing linear matrix inequality based antiwindup synthesis algorithms can be modified to produce compensators that accommodate uncertainty better. Embedded within these results is the ever-present performance - robustness tradeoff. A remarkable feature is that the often criticized internal model control antiwindup solution emerges as an ldquooptimally robustrdquo solution. A simple example demonstrates the effectiveness of the modified algorithms.

State-space formulae for discrete-time H∞ optimization

Abstract State-space formulae and proofs are given for ail the important steps in discrete-time H 8 optimization. The steps closely follow the algorithms for continuous-time systems, but there are some technically involved differences in the detail that make their derivation non-trivial.

Static output feedback stabilisation with H∞ performance for a class of plants

In this paper, the problem of static output feedback control of a linear system is considered. The existence of a static output feedback control law is given in terms of the solvability of two coupled Lyapunov inequalities which result in a non-linear optimisation problem. However, using state-coordinate and congruence transformations and by imposing a block-diagonal structure on the Lyapunov matrix, we will see that the determination of a static output feedback gain reduces, for a specific class of plants, to finding the solution of a system of linear matrix inequalities. The class of plants considered is those which are minimum phase with a full row rank Markov parameter. The method is extended to incorporate H∞ performance objectives. This results in a sub-optimal static H∞ control law found by non-iterative means. The simplicity of the method is demonstrated by a numerical example.

Practical implementation of a novel anti-windup scheme in a HDD-dual-stage servo-system

Two novel discrete anti-windup (AW) techniques are applied to a dual-stage actuator of an experimental hard disk drive system. The techniques, one low order, the other full order, employ convex l/sub 2/-performance constraints in combination with linear-matrix-inequality-optimization methods. It is shown that the AW compensators can improve the performance of the nominal dual-stage servo-system when the secondary actuator control signal saturates at its allowable design limits. Also, stability is achieved despite saturation of both the secondary actuator and the voice-coil-motor actuator. Practical results show that the performance of each AW compensator is superior to another well-known ad-hoc AW technique, the internal model control AW scheme. The main contribution of the paper is the application of theoretically rigorous AW methods to an industrially relevant servo system.

Non-linear tracking control for multivariable constrained input linear systems

This paper extends the non-linear tracking methodology of Lin et al. to high-order and multivariable linear systems. The results provide a method of synthesizing controllers which asymptotically track a constant set-point. As with the original scheme, allowances for control limits are handled directly in the design phase, and no a posteriori compensation is required. The resulting control law consists of both linear and non-linear parts; the non-linear term being added with a view to improving the response of the system, without reducing the size of its basin of attraction. The proposed technique is demonstrated on two aerospace examples which indicate promising results.

Improvements in product quality in tandem cold rolling using robust multivariable control

This paper considers the gauge control problem in tandem cold rolling. A robust multivariable solution is proposed via the H/sup /spl infin// loop shaping method of McFarlane and Glover (1990), which combined with a gain scheduling technique enables the control of the mill from thread speed to full speed. Improvement over a representative industrial controller is observed from nonlinear simulation results.

Pole-zero cancellations and closed-loop properties of an H ∞ mixed sensitivity design problem

Abstract We examine an H ∞ mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions . Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

Real-time path planning with limited information for autonomous unmanned air vehicles

We propose real-time path planning schemes employing limited information for fully autonomous unmanned air vehicles (UAVs) in a hostile environment. Two main algorithms are proposed under different assumptions on the information used and the threats involved. They consist of several simple (computationally tractable) deterministic rules for real-time applications. The first algorithm uses extremely limited information (only the probabilistic risk in the surrounding area with respect to the UAVs current position) and memory, and the second utilizes more knowledge (the location and strength of threats within the UAVs sensory range) and memory. Both algorithms provably converge to a given target point and produce a series of safe waypoints whose risk is almost less than a given threshold value. In particular, we characterize a class of dynamic threats (so-called, static-dependent threats) so that the second algorithm can efficiently handle such dynamic threats while guaranteeing its convergence to a given target. Challenging scenarios are used to test the proposed algorithms.